We prove several identities on homogeneous groups that imply the Hardy and Rellich inequalities for Bessel pairs. These equalities give a straightforward understanding of some of the Hardy and Rellich inequalities as well as the absence of nontrivial optimizers and the existence/nonexistence of “virtual”extremizers.
The second author (the corresponding author) was partially supported by a fellowship from the Pacific Institute for the Mathematical Sciences.
"Hardy and Rellich inequalities with exact missing terms on homogeneous groups." J. Math. Soc. Japan 71 (4) 1243 - 1256, October, 2019. https://doi.org/10.2969/jmsj/80878087